JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## On character amenable Banach algebras

### Tom 193 / 2009

Studia Mathematica 193 (2009), 53-78 MSC: 22D15, 43A20, 43A30, 43A40, 46H20, 46H25. DOI: 10.4064/sm193-1-3

#### Streszczenie

We obtain characterizations of left character amenable Banach algebras in terms of the existence of left $\phi$-approximate diagonals and left $\phi$-virtual diagonals. We introduce the left character amenability constant and find this constant for some Banach algebras. For all locally compact groups $G$, we show that the Fourier–Stieltjes algebra $B(G)$ is $C$-character amenable with $C<2$ if and only if $G$ is compact. We prove that if $A$ is a character amenable, reflexive, commutative Banach algebra, then $A\cong \mathbb C^n$ for some $n\in \mathbb N$. We show that the left character amenability of the double dual of a Banach algebra $A$ implies the left character amenability of $A$, but the converse statement is not true in general. In fact, we give characterizations of character amenability of $L^1(G)^{**}$ and $A(G)^{**}$. We show that a natural uniform algebra on a compact space $X$ is character amenable if and only if $X$ is the Choquet boundary of the algebra. We also introduce and study character contractibility of Banach algebras.

#### Autorzy

• Z. HuDepartment of Mathematics and Statistics
University of Windsor
e-mail
• M. Sangani MonfaredDepartment of Mathematics and Statistics
University of Windsor